Numerical micromagnetics is an essential tool to optimize magnetic storage media, spin electronic devices, such as MRAM and microsensors. The application of these devices requires a profound knowledge of the reversal mechanism. In nanostructured magnets the switching fields and times which are in the order of pico- to nanoseconds are controlled by the geometric shape of the magnets, the intrinsic properties and the orientation and strength of the applied field. The differences of the magnetization reversal processes under various applied field profiles H(t), such as sweep field, constant unidirectional field, pulsed field and rotational field are studied using a 3D hybrid finite element/boundary element micromagnetic model. Thermal fluctuations, defects and other forms of disorder as well as eddy currents occurring during the fast switching process are not included in the simulations. The Gilbert equation of motion is solved to investigate the reversal dynamics of NiFe and Co nanoelements. The damping parameter a(H) drastically influences the critical switching field and time.